MATLAB: How to implement the following

Image Processing Toolboxinner product

What does this means to?

Best Answer

As you note in the tag, that notation is used most often for the inner product, which is a linear functional, a linear operator from vectors (elements of a vector space) to elements in the scalar field.

Since you also have tagged it with Image Processing Toolbox, I'm assuming you mean the MATLAB function dot().

With N-D arrays, dot() returns the inner products along the first nonsingleton dimension, so that

 A = [1 2; 3 4];
 B = [1 4; 5 6];
 dot(A,B)

Gives a 1x2 vector which are the inner products of the columns of A and B.

While

dot(A,B,2)

gives a 2x1 vectors which contains the inner products of the rows of A and B.

Related Solutions

MATLAB: Dot product for complex vector

help dot
 dot  Vector dot product.
    C = dot(A,B) returns the scalar product of the vectors A and B.
    A and B must be vectors of the same length.  When A and B are both
    column vectors, dot(A,B) is the same as A'*B.
    
 dot(A,B), for N-D arrays A and B, returns the scalar product
    along the first non-singleton dimension of A and B. A and B must
    have the same size.

So what are A and B?

A = [1+i 1-i -1+i -1-i];
B = [3-4i 6-2i 1+2i 4+3i];

They are row vectors, complex row vectors. So MATLAB forms the result as:

dot(A,B)
ans =
            1 -          5i
sum(conj(A).*B)
ans =
            1 -          5i

That is, when A and B are both vectors, MATLAB treats them the same as if A and B were column vectors. It effectively thinks of them as both column vectors. Then it forms the result by conjugating A, takes an element-wise product, then sums those terms.

MATLAB: Dot product function in Matlab

    dot(A,B), for N-D arrays A and B, returns the scalar product
    along the first non-singleton dimension of A and B. A and B must
    have the same size.
>> dot(I(:,1),I(:,1))
ans =
     1

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Related Solutions

MATLAB: Dot product for complex vector

MATLAB: Dot product function in Matlab

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